caravan intermittent start

97 Caravan has intermittent start. Turn ignition switch and only get a "click" and sounds of a weak battery. Strong headlights and regular indications though of all electrical components. Replaced battery as a good place to begin. Cycling of ignition switch seems to eventually get a good strong rotation and subsequent start...
Have read many threads of ignition switch failing or starter solonoid contacts failing or even posible loose wiring/short around the starter...has anyone narrowed this down further???